巧用“点在曲线内部”解题

• 作 者: 曾庆宝
• 机 构: 广西富川县民族中学 542700
• 出 处: 高中数学教与学
• 发表日期: 2004年期
• 关键词: 一元二次方程 求解思路 解题过程 参数范围 数形结合 圆半径 公共点 图象分类 程中

我们知道,对于二次曲线f(x,y)=0和平面内一点P0(x0,y0),有如下结论.(1)若P0(x0,y0)在曲线f(x,y)=0的内部,则f(x0,y0)0;(2)若P0(x0,y0)在曲线f(x,y)=0的内部,则过P0(x0,y0)的直线l恒与曲线f(x,y)=0相交.如果充分利用“点在曲线内部”这一结论解题,不仅求解思路清晰、和谐、优美

We know that for the quadratic curve f(x,y)=0 and a point P0(x0,y0) in the plane, we have the following conclusions. (1) If P0(x0,y0) is on the curve f(x,y)=0 Inside, then f (x0, y0) 0; (2) If P0 (x0, y0) is inside the curve f (x, y) = 0, then the line l constant and curve f that pass P0 (x0, y0) (x, y) = 0 intersection. If you make full use of the “point inside the curve” to solve the problem, not only a clear, harmonious and graceful solution